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Pythagoras theorem

Pythagoras theorem for GCSE Religious Studies AQA Higher: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • AQA
  • Religious Studies
  • Higher
  • Spec R5 · R16 · R8
  • 11 min read
  • 8 revision boxes

Introduction

2 boxes
4 min read

What is pythagoras theorem?

Listen to this box

Transcript

A short spoken summary of pythagoras theorem and where it is used.

A spoken walk-through of pythagoras theorem before you read the notes.
Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing pythagoras theorem laid out step by step

The same idea drawn out, so the method is visible.
4 rows

The pythagoras theorem reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Term
Meaning
Example
Common slip
Row 1 column 1
Row 1 column 2
≈160\approx 160
Row 1 column 4
Row 2 column 1
Row 2 column 2
34×25\frac{3}{4} \times \frac{2}{5}
Row 2 column 4
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left
Row 3 column 4
Row 4 column 1
Row 4 column 2
49=7\sqrt{49} = 7
Row 4 column 4

Learning

4 boxes
3 steps

How to work with pythagoras theorem

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing pythagoras theorem laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
  1. Read the question and write down what is being asked for.
  2. Set out the working for pythagoras theorem in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 34×25\frac{3}{4} \times \frac{2}{5}
2 rules

Key facts: Pythagoras theorem

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • Rule 1

    How pythagoras theorem behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How pythagoras theorem behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

    How pythagoras theorem behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
4 steps

How to work with pythagoras theorem

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing pythagoras theorem laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for pythagoras theorem in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
3 rules

Key facts: Pythagoras theorem

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

  • Rule 1

    How pythagoras theorem behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How pythagoras theorem behaves in the 2nd of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 3

    How pythagoras theorem behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left

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Examples

2 boxes
1 marks · worked

Worked example: pythagoras theorem

The examiner marks the working, so a correct answer with no method still drops marks.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
3 marks · worked

Practice question 8: 49=7\sqrt{49} = 7

Practise the routine version until it is automatic, then move to the multi-step questions.

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Common questions

How many marks is pythagoras theorem usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Religious Studies AQA Higher paper?
Yes — it sits in the Reading and comprehension strand.